Question

A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m³ and 400 J/kg.K, respectively. If the bead is considered as a lumped system, the convective heat transfer coefficient (in W/m².K) between the metal bead and the fluid stream is

Accepted Answer

The correct answer is (B) 299.8. For a sphere, V/A=r/3=0.5/3mm≈1.667×10⁻⁴m. (T−T∞)/(Ti−T∞)=(28−20)/(100−20)=0.1. From ln(0.1)=−hAt/(ρVc)=−ht/(ρ(V/A)c): h=−ln(0.1)×ρ(V/A)c/t = 2.3026×8500×1.667×10⁻⁴×400/4.35 ≈ 300.0 W/m².K.

Explanation